# Properties

 Label 20400.dc Number of curves 6 Conductor 20400 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20400.dc1")

sage: E.isogeny_class()

## Elliptic curves in class 20400.dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20400.dc1 20400cx5 [0, 1, 0, -11097608, 14225884788] [2] 393216
20400.dc2 20400cx3 [0, 1, 0, -693608, 222100788] [2, 2] 196608
20400.dc3 20400cx6 [0, 1, 0, -657608, 246220788] [2] 393216
20400.dc4 20400cx2 [0, 1, 0, -45608, 3076788] [2, 2] 98304
20400.dc5 20400cx1 [0, 1, 0, -13608, -571212] [2] 49152 $$\Gamma_0(N)$$-optimal
20400.dc6 20400cx4 [0, 1, 0, 90392, 18036788] [2] 196608

## Rank

sage: E.rank()

The elliptic curves in class 20400.dc have rank $$1$$.

## Modular form 20400.2.a.dc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4q^{11} + 2q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.